Case 1.—So much heat is supplied to the air during expansion that the temperature remains constant. Hyperbolic expansion.
Then
pv = p1v1.
Work done during expansion per pound of air
= ∫v2v1 p dv = p1v1 ∫v2v1 dv/v
= p1v1 logε v2 / v1 = p1v1 logε p1 / p2.
(1)
Since the weight per cubic foot is the reciprocal of the volume per pound, this may be written
(p1/G1) logε G1/G2.
(1a)